package a10_动态规划;

/**
 * <p>
 * a06_不同路径
 * </p>
 *
 * @author flyduck
 * @since 2025/1/21
 */
public class a06_不同路径 {

    public static void main(String[] args) {
        int i = uniquePaths(3, 2);
        System.out.println();
    }
    //dp[i,j]：代表到达[i,j]有多少种路径
    //递推公式：dp[i,j] = dp[i-1,j] + dp[i,j-1]
    //初始化：dp[0,j] = 1 dp[i,0] = 1
    public static int uniquePaths(int m, int n) {
        int[][] dp = new int[m][n];

        //初始化
        for (int i = 0; i < m; i++) {
            dp[i][0] = 1;
        }

        for (int j = 0; j < n; j++) {
            dp[0][j] = 1;
        }

        for (int j = 1; j < n; j++) {
            for (int i = 1; i < m; i++) {
                dp[i][j] = dp[i-1][j] + dp[i][j-1];
            }
        }
        return dp[m-1][n-1];
     }
}
